---
title: "factorial"
slug: "dev-database-reference-sql-functions-numeric-factorial"
updated: 2026-10-30T18:18:51Z
published: 2026-10-30T18:18:51Z
canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-factorial"
---

> ## Documentation Index
> Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt
> Use this file to discover all available pages before exploring further.

# factorial

*Applies to VAST Cluster 5.5.*

*[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Arithmetic.* `factorial(n)` returns n! = 1 × 2 × … × n, as a 128-bit integer (`HUGEINT`). The postfix operator `n!` is the same function. It takes an `INTEGER` or a smaller integer type, and the largest result is 33!.

## Syntax

```
factorial(n)
n!
```

| Argument | Type | Description |
| --- | --- | --- |
| `n` | `INTEGER`, `SMALLINT` or `TINYINT` | The number to take the factorial of. `BIGINT`, `UINTEGER`, `DECIMAL` and floating-point values aren't accepted; cast them to `INTEGER`. |

**Returns:** `HUGEINT`, a 128-bit integer. The ADBC driver returns it as a `DECIMAL(38,0)`, which Python prints as a `Decimal`.

**Aliases:** the postfix operator `n!`.

## Set up the examples

The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_factorial`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see.

This block connects, defines the `run()` and `plan()` helpers, and creates a table of three relay teams: the number of runners as an `INTEGER`, and the same number as a `BIGINT`. The last row has no values:

```
import os
import re

import adbc_driver_manager
import adbc_driver_manager.dbapi as dbapi
import adbc_driver_vastdb

BUCKET = os.environ["VASTDB_BUCKET"]
SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_factorial"'

conn = dbapi.connect(
    driver=adbc_driver_vastdb.get_driver_path(),
    db_kwargs={
        "vast.db.endpoint": os.environ["QE_ENDPOINT"],
        "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"],
        "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"],
    },
    autocommit=True,
)

def server_message(e):
    """The server's message in a driver error, without the request ID or the echoed statement."""
    text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e))
    found = (re.search(r'message: "(.*?)", request_id', text, re.S)
             or re.search(r"description: (.*)\)", text, re.S))
    message = found.group(1) if found else text.strip().splitlines()[-1]
    message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S)
    message = re.split(r"\\n|\n", message)[0].replace('\\"', '"')
    return message.replace(BUCKET, "<bucket>")

def run(sql):
    """Run one statement. Print the rows it returns, or the error."""
    try:
        with conn.cursor() as cur:
            cur.execute(sql)
            rows = cur.fetchall() if cur.description else []
    except (adbc_driver_manager.Error, OSError) as e:
        print(f"{type(e).__name__}: {server_message(e)}")
    else:
        print(rows)

def plan(sql):
    """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert."""
    with conn.cursor() as cur:
        cur.execute("EXPLAIN " + sql)
        steps = cur.fetchall()[0][1]
    print("\n".join(line for line in steps.splitlines() if "Rows" not in line))

TABLE = f"{SCHEMA}.teams"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, runners INTEGER, runners_big BIGINT)")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, 4, 4), "
    "(2, 5, 5), "
    "(3, 0, 0), "
    "(4, NULL, NULL)")
```

```
[]
[]
[(4,)]
```

## What it does

`factorial(n)` multiplies the whole numbers from 1 to `n`. It's the number of ways to put `n` things in order: 4 runners can run a relay in 4! = 24 orders.

- **0! and 1! are 1,** and so is the factorial of any negative number: `factorial(-5)` is 1.
- **The result is a `HUGEINT`,** so it holds 20! (2432902008176640000), which is past the `BIGINT` range at 21!, up to 33! (8683317618811886495518194401280000000). `factorial(34)` stops the query with `Value out of range`.
- **The argument must be an `INTEGER` or smaller.** A `BIGINT` column fails with `No function matches the given name and argument types &apos;factorial(BIGINT)&apos;`; cast it: `factorial(CAST(n AS INTEGER))`. A numeric string is converted: `factorial(&apos;12&apos;)` is 479001600.

### The postfix `!` operator

`n!` is the same function. `5!`, `5 !` and `(5)!` are all 120, and `(2 + 3)!` is 120. Two things to watch:

- **A minus sign is applied first:** `-(5)!` is `(-5)!`, which is 1, not -120.
- **`!` can't be followed by another operator:** `(5)! + 1` fails with `Scalar Function with name ! does not exist!`. Use `factorial(5) + 1`, or keep `!` at the end of the expression: `factorial(5) = (5)!` works.

## NULLs and edge cases

| Input | Result |
| --- | --- |
| `factorial(NULL)`, `(NULL)!` | `NULL` |
| `factorial(0)`, `factorial(1)` | `1`, `1` |
| `factorial(-1)`, `factorial(-5)` | `1`, `1` |
| `factorial(5)`, `typeof(factorial(5))` | `120`, `HUGEINT` |
| `factorial(20)`, `factorial(21)` | `2432902008176640000`, `51090942171709440000` |
| `factorial(33)` | `8683317618811886495518194401280000000` |
| `factorial(34)` | Error: `Value out of range` |
| `5!`, `5 !`, `(5)!`, `(2 + 3)!` | `120` each |
| `-(5)!` | `1` |
| `(5)! + 1` | Error: `Scalar Function with name ! does not exist!` |
| `factorial(5::TINYINT)`, `factorial(&apos;12&apos;)` | `120`, `479001600` |
| `factorial(5::BIGINT)`, `factorial(5::UINTEGER)` | Error: `No function matches the given name and argument types` |
| A `DECIMAL`, `DOUBLE`, date, boolean, `BLOB` or list | Error: `No function matches the given name and argument types` |

The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-factorial#set-up-the-examples):

```
run("SELECT factorial(NULL), (NULL)!, factorial(0), factorial(1), factorial(-1), factorial(-5)")
run("SELECT factorial(5), typeof(factorial(5)), factorial(20), factorial(21), factorial(33)")
run("SELECT factorial(34)")
run("SELECT 5!, 5 !, (5)!, (2 + 3)!, -(5)!, factorial(5) = (5)!")
run("SELECT (5)! + 1")
run("SELECT factorial(5::TINYINT), factorial('12')")
run("SELECT factorial(5::BIGINT)")
run("SELECT factorial(5::UINTEGER)")
run("SELECT factorial(1.5)")
```

```
[(None, None, Decimal('1'), Decimal('1'), Decimal('1'), Decimal('1'))]
[(Decimal('120'), 'HUGEINT', Decimal('2432902008176640000'), Decimal('51090942171709440000'), Decimal('8683317618811886495518194401280000000'))]
OSError: Value out of range
[(Decimal('120'), Decimal('120'), Decimal('120'), Decimal('120'), Decimal('1'), True)]
InternalError: Catalog Error: Scalar Function with name ! does not exist!
[(Decimal('120'), Decimal('479001600'))]
InternalError: Binder Error: No function matches the given name and argument types 'factorial(BIGINT)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'factorial(UINTEGER)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'factorial(DECIMAL(2,1))'. You might need to add explicit type casts.
```

## Examples

The number of running orders for each team, with `factorial()` and with `!`:

```
run(f"SELECT id, runners, factorial(runners), (runners)! FROM {TABLE} ORDER BY id LIMIT 10")
```

```
[(1, 4, Decimal('24'), Decimal('24')), (2, 5, Decimal('120'), Decimal('120')), (3, 0, Decimal('1'), Decimal('1')), (4, None, None, None)]
```

A `BIGINT` column has to be cast first:

```
run(f"SELECT id, factorial(runners_big) FROM {TABLE} ORDER BY id LIMIT 10")
run(f"SELECT id, factorial(CAST(runners_big AS INTEGER)) FROM {TABLE} ORDER BY id LIMIT 10")
```

```
InternalError: Binder Error: No function matches the given name and argument types 'factorial(BIGINT)'. You might need to add explicit type casts.
[(1, Decimal('24')), (2, Decimal('120')), (3, Decimal('1')), (4, None)]
```

Keep only the teams with exactly 120 running orders:

```
run(f"SELECT id, runners FROM {TABLE} WHERE factorial(runners) = 120 ORDER BY id LIMIT 10")
```

```
[(2, 5)]
```

## How it runs in VAST

The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `factorial()` is always computed by the Query Engine:

- **In the `SELECT` list,** the scan reads the column and the Query Engine computes `factorial()` for each row it returns.
- **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `factorial()` and keeps the rows that match. No rows are skipped in storage.

A run-time error on any row cancels the whole query: if one row holds 34 or more, `factorial()` of that column fails with `Value out of range`, even when you want the other rows.

The plan of the `WHERE` example shows the `FILTER` step above the scan:

```
plan(f"SELECT id FROM {TABLE} WHERE factorial(runners) = 120")
```

```
┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│ (factorial(runners) = 120)│
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│          runners          │
│             id            │
│                           │
└───────────────────────────┘
```

## Make it faster

- **Compare the argument, not the factorial.** Factorials of positive numbers grow with `n`, so `factorial(runners) = 120` is the same as `runners = 5` for positive values, and that comparison is pushed down to VAST DataBase. The plan has no `FILTER` step:

```
plan(f"SELECT id FROM {TABLE} WHERE runners = 5")
```

```
┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘
```

- **Keep values of 34 or more away from `factorial()`.** One such row fails the whole query. Check the column's largest value first, for example with `max(runners)`. A guard such as `CASE WHEN runners &lt;= 33 THEN factorial(runners) END` is shown in [Limitations and errors](/develop/docs/dev-database-reference-sql-functions-numeric-factorial#limitations-and-errors).

## Limitations and errors

- **33! is the largest result.** `factorial(34)` and anything larger fail with `Value out of range`, and one such row cancels the query. For large `n`, use [lgamma](/develop/docs/dev-database-reference-sql-functions-numeric-lgamma): `lgamma(n + 1)` is the natural logarithm of n!, as a `DOUBLE`.
- **`INTEGER` or smaller only.** `BIGINT`, `UINTEGER`, `DECIMAL`, `DOUBLE` and `FLOAT` fail with `No function matches the given name and argument types`. Cast to `INTEGER`. For a non-integer, use [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma): `gamma(x + 1)` is the factorial of `x` for whole numbers, as a `DOUBLE`.
- **Negative numbers give 1,** not an error or NULL.
- **The postfix `!` can't be followed by another operator.** See [The postfix ! operator](/develop/docs/dev-database-reference-sql-functions-numeric-factorial#the-postfix-operator).

```
run(f"SELECT id, CASE WHEN runners <= 33 THEN factorial(runners) END FROM {TABLE} ORDER BY id LIMIT 10")
run("SELECT factorial(5) + 1, lgamma(35)")
```

```
[(1, Decimal('24')), (2, Decimal('120')), (3, Decimal('1')), (4, None)]
[(Decimal('121'), 88.58082754219767)]
```

## Similar functions

| Function | Does | Result for 5 (or 6 for `gamma`) |
| --- | --- | --- |
| `factorial(n)`, `n!` | n!, exactly, as a `HUGEINT` | `120` |
| [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma) | the gamma function: `gamma(n + 1)` is n!, as a `DOUBLE` | `120.0` |
| [lgamma](/develop/docs/dev-database-reference-sql-functions-numeric-lgamma) | the natural logarithm of the gamma function | `exp(lgamma(6))` is `119.99999999999997` |

```
run("SELECT factorial(5), (5)!, gamma(6), exp(lgamma(6))")
```

```
[(Decimal('120'), Decimal('120'), 120.0, 119.99999999999997)]
```

Clean up:

```
run(f"DROP TABLE IF EXISTS {TABLE}")
run(f"DROP SCHEMA IF EXISTS {SCHEMA}")
conn.close()
```

```
[]
[]
```

## See also

- [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric#arithmetic): all the arithmetic functions.
- [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma), [lgamma](/develop/docs/dev-database-reference-sql-functions-numeric-lgamma) and [gcd](/develop/docs/dev-database-reference-sql-functions-numeric-gcd).
- [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns).
- [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.